Van Nistelrooy was placed in charge of Man United on an interim basis after Erik ten Hag was sacked, and the Dutchman guided the team to a 5-2 success over Leicester City in the last-16 stage of the EFL Cup last week.
The Red Devils were then in Premier League action against Chelsea on Sunday, playing out a 1-1 draw with the Blues.
Van Nistelrooy has two more games at the helm - a Europa League clash with PAOK on Thursday night, in addition to a Premier League fixture with Leicester on Sunday afternoon.
Amorim will officially take charge on November 11, and the current Sporting Lisbon head coach has confirmed that he will be bringing staff members with him to Old Trafford.
Van Nistelrooy yet to speak with Amorim over his plans
Van Nistelrooy has expressed a desire to remain with Man United as a part of the new set-up, and he recently suggested that he is expecting to revert to his assistant manager role once Amorim has arrived.
However, the club's former striker said ahead of Thursday's European game with PAOK that he is yet to speak with Amorim, who will take charge of his final game as Sporting manager against Braga this weekend.
"No, I didn't have contact, so far. So no changes in that. I don't know when yet either. It is difficult to comment on that now. I'm waiting for conversations to take place and, in the meantime, obviously the one thing that is the most important thing for this football club now is getting the work done, on a daily basis, and the game coming up tomorrow in Europe," Van Nistelrooy told reporters during his pre-match press conference.
"A European night at Old Trafford, against the Greek champions, second in the league currently. I welcome Ruben, I'm here to help him and that is the situation at the moment.
"I'm focusing on the players that are currently fit. That's my job, [to] manage them as good as I can. I'm so focused on today and tomorrow, to do well for the short spell I'm responsible for this football club. I take that as a big responsibility."
Van Nistelrooy calls PAOK clash "high priority"
Man United have drawn their three Europa League matches this season against FC Twente, Porto and Fenerbahce, which has left them down in 21st spot in the Europa League table.
"Like I commented before, the game is of high priority for us tomorrow. We don't look past the game to further games. We know we need all our attention on PAOK," added the interim head coach.
"We analysed them very well. We know they're the current champions, PAOK, and it's a big achievement. They're second behind Aris at the moment and have lots of talented players, experienced players and a strong side. They will be supported with 4,000 fans travelling and supporting the team. We are ready to face a very tough game tomorrow."
Man United have five more games in the league phase of the Europa League, with the team also set to take on Bodo/Glimt (H), Viktoria Plzen (A), Rangers (H) and FCSB (A).